PYQ Vault
EbooksTutor

Orthocentre, centroid and circumcentre: H, G, O are collinear with OH = 3 OG

This type of question, asked 2 times: 10 Apr 2023, 24 Jan 2025. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    10 Apr 2023

    163
    If the points PP and QQ are respectively the circumcentre and the orthocentre of a △ABC\bigtriangleup ABC, then PA→+PB→+PC→\overrightarrow{PA}+\overrightarrow{PB}+\overrightarrow{PC} is equal to

    Tap an option to check your answer.

  2. Question 2

    24 Jan 2025

    131
    Let the position vectors of three vertices of a triangle be 4p→+q→−3r→,−5p→+q→+2r→4\overrightarrow{p}+\overrightarrow{q}- 3\overrightarrow{r}, - 5\overrightarrow{p}+\overrightarrow{q}+ 2\overrightarrow{r} and 2p→−q→+2r→2\overrightarrow{p}-\overrightarrow{q}+ 2\overrightarrow{r}. If the position vectors of the orthocenter and the circumcenter of the triangle are p→+q→+r→4\frac{\overrightarrow{p}+\overrightarrow{q}+\overrightarrow{r}}{4} and αp→+βq→+γr→\alpha\overrightarrow{p}+\beta\overrightarrow{q}+\gamma\overrightarrow{r} respectively, then α+2β+5γ\alpha+ 2\beta+ 5\gamma is equal to:

    Tap an option to check your answer.